We can apply an average operation to two vectors: \(\mathbf {\tau }_x\)  in Line 7 and \(|\mathbf {\Phi }^H |^{.2} \mathbf {\tau }_s\)  in Line 5 of blackUAMPv1 in Algorithm REF , leading to the second version of UAMP [1]} black(called UAMPv2), where the operations in the brackets of Lines 1, 5 and 7 are executed (refer to [2]} for the derivation).
Compared to AMP and blackUAMPv1, UAMPv2 does not require matrix-vector products in Lines 1 and 5, so that the number of matrix-vector products is reduced from 4 to 2 per iteration. This is a significant reduction in computational complexity because the complexity of AMP-like algorithms is dominated by matrix-vector products.
